Exploratory Analysis
First we will have a look at the variables in their raw form as found in the dataset.
The measurements for temperature show a strong annual effect where the temperatures reach the lowest in January, and becomes warmer throughout the year until a turning point is reached roughly around June after which it descends. The changes in temperature are generally smooth with the only concerning feature thus far being the double peak event that seems to occur in the first, third and fourth years.
Humidity also has a strong annual seasonal pattern. The highest level occurs during the start of the year after which there is a steady decline reaching it’s lowest level around early May. The humidity then rises until it reaches a peak roughly around July-August after which it declines until the months of October-November then rises finally to the high-point in January. A concern may be the shifting of the period in between the double peak. Another may be that the humidity magnitudes for the double peaks seem to be approaching the same value through the years. The values seem to vary about the trend to a large degree.
The wind speed data has an annual seasonal trend that is similar to that of the temperature data in terms of it’s behavior across the months but instead has the lowest speeds occurring during the months of November-December. There are a few instances where the wind speed does exceed that of the trend and these don’t seem to be affiliated with any specific calendar based time period.
The initial view for the pressure data is not very helpful as there are several data points that require inspection.
Application of Logarithm Transformation with offset
In order to show the pattern within the Pressure data the most troubling outliers were inspected and removed. This will be detailed in the next section for the other variables. The data was checked via " " which hosts historical and current climate and weather data for Dehli.
The pattern for the wind speed is not more concretely seen after the log transformation.
Correlation Plots
The temperature variable seems have a strong decaying correlation between the lags. It also seems that after the zero and first lag are controlled for, subsequent lags do not hold much more information about the series as even the seasonal component is removed. Lags 2, 3 and 4 may be included in the model but it is doubtful that this will improve the fit.
A similar process seems to hold true for the Humidity variable.
There exists correlation present between the lagged values of Wind Speed that is of a rapidly decaying nature and is much weaker than the correlation found in both the Temperature and Humidity data.
There exists correlation between the lags of the Pressure variable that is of a gentle decreasing nature comparable to that of the Temperature and Humidity Data. In this case the third lag may be of interest.
The above plot will allow us to understand how Humidity, Wind Speed and Pressure vary with Temperature. Humidity has a moderate, negative and gently decaying correlation effect with Temperature (starting at -0.57). Wind Speed has a weak, positive and gently decaying correlation effect with Temperature (the effect sizes start at 0.27). Pressure has a strong negative gently decaying correlation effect with Temperature (starting at -0.86).
Seasonal Diagnositcs
Each of the time series data indicate a seasonal pattern for the month, but not for any other calendar based time feature such as the week day or year. This is consistent with the description in the first section that showed a consistent pattern within each year.
I suggest you use the interactive selection of the plots in order to focus directly on the boxplots so the any outlier effects will diminish.
Anomalies/Outliers
The time stamps identified in the above plots were all checked for validity. It is the case that all of the Pressure data anomalies were resolved. See the outlier table in the appendix for the details on all points.
Season Trend by Loess Decomposition
Standardized Plot for all Time Series